Existence of positive solutions for $n \times n$ cycled systems of nonlinear differential equations associated with degenerated $p$-Laplacians

Abstract

We investigate the existence, multiplicity and nonexistence of positive solutions to $n\times n$ cycled systems of nonlinear differential equations with degenerated $p$-Laplacians and nonlinearities satisfying combined $p$-linear condition at $0$ and combined $p$-sublinear, $p$-superlinear or $p$-linear condition at $\infty$. In particular, the existence of at least three positive solutions is discussed. This is even new for $n\times n$ cycled systems of nonlinear differential equations with degenerated Laplacians. We carry on only one fixed point theorem for proofs of all cases.